New findings for the old problem: Exact solutions for domain walls in coupled real GinzburgLandau equations
Abstract
This work reports new exact solutions for domainwall (DW) states produced by a system of coupled real GinzburgLandau (GL) equations which model patterns in thermal convection, optics, and BoseEinstein condensates (BECs). An exact solution for symmetric DW was known for a single value of the crossinteraction coefficient, G = 3 (defined so that its selfinteraction counterpart is 1). Here an exact asymmetric DW is obtained for the system in which the diffusion term is absent in one component. It exists for all G > 1. Also produced is an exact solution for DW in the symmetric realGL system which includes linear coupling. In addition, an effect of a trapping potential on the DW is considered, which is relevant to the case of BEC. In a system of three GL equations, an exact solution is obtained for a composite state including a twocomponent DW and a localized state in the third component. Bifurcations which create two lowest composite states are identified too. Lastly, exact solutions are found for the system of real GL equations for counterpropagating waves, which represent a sink or source of the waves, as well as for a system of three equations which includes a standing localized component.
 Publication:

Physics Letters A
 Pub Date:
 January 2022
 DOI:
 10.1016/j.physleta.2021.127802
 arXiv:
 arXiv:2110.14522
 Bibcode:
 2022PhLA..42227802M
 Keywords:

 RayleighBénard convection;
 Pattern formation;
 Lyapunov functional;
 Grain boundary;
 ThomasFermi approximation;
 Linear coupling;
 Nonlinear Sciences  Pattern Formation and Solitons;
 Condensed Matter  Quantum Gases;
 Physics  Optics
 EPrint:
 Physics Letters A, in press